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Normal Criterion for Families of Meromorphic Functions and Shared Functions

Author

Listed:
  • Ai Huang

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China)

  • Jinhua Yang

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, China)

Abstract

This paper broadens the scope of existing research: the shared value is generalized from a non-zero finite complex number to a non-identically zero holomorphic function, the order of the derivative is extended from the first order to an arbitrary k -th order, and the constraint condition on the polynomial H is simplified to deg H ≥ 2 . A more general normality criterion for families of meromorphic functions involving the sharing of differential polynomials is proved. Let D be a domain, F be a family of meromorphic functions in D , and P ( z ) be a non-identically zero holomorphic function in D . If for any f , g ∈ F , the differential polynomials H ( f ) f ( k ) and H ( g ) g ( k ) share P ( z ) in D , then F is normal in D .

Suggested Citation

  • Ai Huang & Jinhua Yang, 2026. "Normal Criterion for Families of Meromorphic Functions and Shared Functions," Mathematics, MDPI, vol. 14(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:2:p:353-:d:1844952
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